From: Oliver Steinkamp <ollis@math.uni-bremen.de>
Newsgroups: sci.math.research
Subject: Re: Brownian motion / joint density
Date: Tue, 10 Nov 1998 09:23:05 +0100

Aaron Brask wrote:

> I am looking to obtain a joint density function for:
> B_t, M_t, and m_t  where:
> B_t = std. linear BM
> M_t = sup{s<t} B_s   (i.e. running max)
> M_t = inf{s<t} B_s   (i.e. running min)

See
Handbook of Brownian motion - facts and formulae
Andrei N. Borodin; Paavo Salminen
Birkhaeuser,Basel, Boston,1996
ISBN: 3-7643-5463-1 (Basel ...) : 0-8176-5463-1 (Boston)

in particular formula 28 (p. 123), resp., 1.28.x (p.161f)

Regards,

Oliver Steinkamp

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Oliver Steinkamp        E-mail: ollis***nospam***@math.uni-bremen.de
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